Siegel's theorem and the abc conjecture
Received: 2 March 2004 Revised: 1 September 2004
Mathematics Subject Classification (2000): 11G30 - 11J25 - 11G50
Abstract: Following N. Elkies elkies we show that the abc conjecture of Masser-Oesterlé implies an effective version of Siegel's theorem about integral points on algebraic curves, i.e. an upper bound for the S-integral points where the dependence on S is explicit. The converse statement is also announced in this note. For both results, the main geometric tool is a theorem of G.V. Belyi.